On System Stability under Random Perturbations

In this paper we concider the problem of stability of stochastic evolution systemsin Hilbert space drived by a cylindrical Brownian mothin. We regard the stochestic evolutionequation dXt = AXtdt +G(Xt)dBt as a deterministic system of the form dXt=AXtdt under randomperturbation,and obtain stability of its solution. It is shown that under certain assumptions,itsevolution solution and L2-contimuous evulution solution are exponertially stable.     

Prediction of the Economic Development for the Circumjacent Reservoir Region of the Longtan Hydropower Project Using Grey Quantitative Analog

In order to overcome some technical difficulties,we adopt ingenously the grey models combined with the quantitative analog method,and select the Dan Jiangkou Project which has accumulated practical operation data for a long time as the analog project to predict the economic influence for the circumjacent reservoir region of the Longtan hydropower project.On the basis of analog we have built various industrial economic grey models,and compare them with the corresponding predictions for the unconstructed reservoir case.The predictions of the former are greatly larger than the later ones.and hence provides a certain scientific basis for the central leaders to make a decision for constructing the huge hydropower project ultimateiy.     

The Feasible Control for the Day-operation of the Three-Gorge Cascade Hydropower Station

The feasible control problem is presented for the day-operation of the Three-Gorge Caseade Hydropower Station. The significance of the problem is explained. Basic propetties ofthe problem and the approaches to study it are discussed. Two methfods are given for solving theproblem. which are calculus of variation and linear programming. In the former. the Euler equationwith time-lag and the generalised two-point boundary conditions are obtained and the correspondingpractical implication is interpreted. In the latter. the rationality for the discrete model is exptainedand the computalional details are given for the implement software. some questions which should bepaid much attentfon and the corresponding propeels are prasented based on the numerical results andtheoretical analysis     

Weighting Coefficient Optimization Unification of Lexicographic Method in Fuzzy Multi -objective Optimization Design

The Lexicographic method has subjective and empirical character,so a weighting coefficient is introduced by considering the importance and proportion of each individual object,the preferable result of every individual object can be confirmed by comparing the degree of similarity between the perfect one and the ecumenic one and the Fuzzy optimization will be perfect.The effectiveness of these methods is illustrated by a fuzzy optimal design of the three-bar truss.     

A Class of Exact Solution for RLW-Burgers Equation

A class of analytic solution for RLW Burgers equation and KdV Burgers equation are given which include results of some papers.These solutions can be expressed as some linear combination of solutions of Burgers equation and RLW equation or KdV equation which correct conclusion in some paper.     

Asymptotic Attractors of the Nonlinear Evolution Equation in Bounded Domain

The basic principle of infinite-dimensional dynamic system is to try to reduce the original infinite-dimensional system to an infinite-dimensional system. However,due to the unknown structure of the reduced system, it is difficult to describe its dynamical behaviour. To overcome this difficulty, the idea of approximate inertial manifolds is introduced, for NSE, the existence of AIM was studied, it is shown that the global attractor lies within a neighborhood of the graph of an Lipschitz function by the squeezing property. In this paper, by constructing a finite dimensional solution sequence, we will prove that it tends to the global attractor, theoretically, this provides a metod of constructing the asymptotic attractors, theoretically, this provides a method of constructing the asymptotic attractors for the evolution equations.